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Multiple Choice
Find the area under the curve in the function below from to .
A
34
B
38
C
50
D
42
Verified step by step guidance
1
Identify the shape of the area under the curve from x = -2 to x = 8. The graph shows a trapezoid with two parallel sides and two non-parallel sides.
Determine the coordinates of the vertices of the trapezoid. From the graph, the vertices are approximately (-2, 4), (2, 4), (6, 4), and (8, 0).
Calculate the lengths of the parallel sides of the trapezoid. The parallel sides are horizontal lines from (-2, 4) to (2, 4) and from (2, 4) to (6, 4), both having a length of 4 units.
Calculate the height of the trapezoid, which is the vertical distance between the parallel sides. The height is the y-coordinate difference from 4 to 0, which is 4 units.
Use the formula for the area of a trapezoid: \( A = \frac{1}{2} \times (b_1 + b_2) \times h \), where \( b_1 \) and \( b_2 \) are the lengths of the parallel sides, and \( h \) is the height. Substitute the values to find the area.